Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 2.6, Problem 52E
An experimenter wishes to investigate the effect of three variables—pressure, temperature, and the type of catalyst—on the yield in a refining process. If the experimenter intends to use three settings each for temperature and pressure and two types of catalysts, how many experimental runs will have to be conducted if he wishes to run all possible combinations of pressure, temperature, and types of catalysts?
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b. An experiment wishes to investigate the effect of three variables- pressure, temperature, and the type
of catalyst on the yield in a refining process. if the experimenter intends to use three setting each for
temperature and pressure and two types of catalyst. How many experimental runs will have to be
conducted?
DDT (dichlorodiphenyltrichloroethane) was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 200 kilograms of DDT that has seeped into the soil.
t = time in yearssince application
D = DDT remaining,kilograms
0
200.00
1
190.00
2
180.50
3
171.48
(a) Show that the data are exponential.
The ratio from year 0 to year 1 is ______ , from year 1 to year 2 is ____ , and from year 2 to year 3 is_____ (rounded to two decimal places). Because these successive ratios are all , a) different b)the same , the data are exponential.
A certain reaction was run several times using each of the two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product.Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:Catalyst A Catalyst B4.4 3.4 2.6 3.8 3.4 1.1 2.9 5.54.9 4.6 5.2 4.7 6.4 5.0 5.8 2.54.1 2.6 6.7 4.1 3.7 3.8 3.1 1.63.6 2.9 2.6 4.0 3.5 5.9 6.7 5.24.3 3.9 4.8 4.5 6.3 2.6 4.3 3.84.4 3.1 5.7 4.5a. Construct comparative boxplots for the yields of the two catalysts and explain the role the whisker plays in data analysis. b. Interpret what the box plot for catalyst B, communicate in real life? marc. In your own words, give a simple explanation on why statisticians think the sample variance is biased estimator of the population variance and how it could be corrected.
Chapter 2 Solutions
Mathematical Statistics with Applications
Ch. 2.3 - Suppose a family contains two children of...Ch. 2.3 - Suppose that A and B are two events. Write...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Refer to Exercise 2.4. Use the identities...Ch. 2.3 - Suppose two dice are tossed and the numbers on the...Ch. 2.3 - A group of five applicants for a pair of identical...Ch. 2.3 - From a survey of 60 students attending a...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...
Ch. 2.4 - A sample space consists of five simple events. E1,...Ch. 2.4 - A vehicle arriving at an intersection can turn...Ch. 2.4 - Americans can be quite suspicious, especially when...Ch. 2.4 - A survey classified a large number of adults...Ch. 2.4 - An oil prospecting firm hits oil or gas on 10% of...Ch. 2.4 - Prob. 16ECh. 2.4 - Hydraulic landing assemblies coming from an...Ch. 2.4 - Suppose two balanced coins are tossed and the...Ch. 2.4 - A business office orders paper supplies from one...Ch. 2.4 - The following game was played on a popular...Ch. 2.4 - If A and B are events, use the result derived in...Ch. 2.4 - If A and B are events and B A, use the result...Ch. 2.4 - Prob. 23ECh. 2.4 - Use the result in Exercise 2.22 and the Axioms in...Ch. 2.5 - A single car is randomly selected from among all...Ch. 2.5 - According to Websters New Collegiate Dictionary, a...Ch. 2.5 - In Exercise 2.12 we considered a situation where...Ch. 2.5 - Four equally qualified people apply for two...Ch. 2.5 - Two additional jurors are needed to complete a...Ch. 2.5 - Three imported wines are to be ranked from lowest...Ch. 2.5 - A boxcar contains six complex electronic systems....Ch. 2.5 - A retailer sells only two styles of stereo...Ch. 2.5 - The Bureau of the Census reports that the median...Ch. 2.5 - Patients arriving at a hospital outpatient clinic...Ch. 2.6 - An airline has six flights from New York to...Ch. 2.6 - Prob. 36ECh. 2.6 - A businesswoman in Philadelphia is preparing an...Ch. 2.6 - An upscale restaurant offers a special fixe prix...Ch. 2.6 - An experiment consists of tossing a pair of dice....Ch. 2.6 - A brand of automobile comes in five different...Ch. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - A fleet of nine taxis is to be dispatched to three...Ch. 2.6 - Refer to Exercise 2.43. Assume that taxis are...Ch. 2.6 - Prob. 45ECh. 2.6 - Ten teams are playing in a basketball tournament....Ch. 2.6 - Refer to Exercise 2.46. If 2n teams are to be...Ch. 2.6 - Prob. 48ECh. 2.6 - Students attending the University of Florida can...Ch. 2.6 - Prob. 50ECh. 2.6 - A local fraternity is conducting a raffle where 50...Ch. 2.6 - An experimenter wishes to investigate the effect...Ch. 2.6 - Five firms, F1, F2,, F5, each offer bids on three...Ch. 2.6 - A group of three undergraduate and five graduate...Ch. 2.6 - A study is to be conducted in a hospital to...Ch. 2.6 - A student prepares for an exam by studying a list...Ch. 2.6 - Two cards are drawn from a standard 52-card...Ch. 2.6 - Five cards are dealt from a standard 52-card deck....Ch. 2.6 - Prob. 59ECh. 2.6 - Refer to Example 2.7. Suppose that we record the...Ch. 2.6 - Prob. 61ECh. 2.6 - A manufacturer has nine distinct motors in stock,...Ch. 2.6 - The eight-member Human Relations Advisory Board of...Ch. 2.6 - A balanced die is tossed six times, and the number...Ch. 2.6 - Prob. 65ECh. 2.6 - Refer to Example 2.10. What is the probability...Ch. 2.6 - Refer to Example 2.13. Suppose that the number of...Ch. 2.6 - Show that, for any integer n 1, a (nn)=1....Ch. 2.6 - Prob. 69ECh. 2.6 - Prob. 70ECh. 2.7 - If two events, A and B, are such that P(A) = .5,...Ch. 2.7 - For a certain population of employees, the...Ch. 2.7 - Gregor Mendel was a monk who, in 1865, suggested a...Ch. 2.7 - One hundred adults were interviewed in a telephone...Ch. 2.7 - Prob. 75ECh. 2.7 - A survey of consumers in a particular community...Ch. 2.7 - A study of the posttreatment behavior of a large...Ch. 2.7 - In the definition of the independence of two...Ch. 2.7 - Suppose that A and B are mutually exclusive...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If P(A) 0, P(B) 0, and P(A) P(A|B), show that...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If A and B are mutually exclusive events and P(B) ...Ch. 2.8 - If A1, A2, and A3 are three events and...Ch. 2.8 - Prob. 85ECh. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Prob. 89ECh. 2.8 - Suppose that there is a 1 in 50 chance of injury...Ch. 2.8 - Can A an B be mutually exclusive if P(A) = .4 and...Ch. 2.8 - Prob. 92ECh. 2.8 - In a game, a participant is given three attempts...Ch. 2.8 - A smoke detector system uses two devices, A and B....Ch. 2.8 - Prob. 95ECh. 2.8 - If A and B are independent events with P(A) = .5...Ch. 2.8 - Consider the following portion of an electric...Ch. 2.8 - With relays operating as in Exercise 2.97, compare...Ch. 2.8 - Suppose that A and B are independent events such...Ch. 2.8 - Show that Theorem 2.6, the additive law of...Ch. 2.8 - Articles coming through an inspection line are...Ch. 2.8 - Diseases I and II are prevalent among people in a...Ch. 2.8 - Refer to Exercise 2.50. Hours after the rigging of...Ch. 2.8 - If A and B are two events, prove that...Ch. 2.8 - If the probability of injury on each individual...Ch. 2.8 - If A and B are equally likely events and we...Ch. 2.8 - Prob. 107ECh. 2.8 - If A, B, and C are three events, use two...Ch. 2.8 - Prob. 109ECh. 2.9 - Of the items produced daily by a factory, 40% come...Ch. 2.9 - Prob. 111ECh. 2.9 - Three radar sets, operating independently, are set...Ch. 2.9 - Consider one of the radar sets of Exercise 2.112....Ch. 2.9 - A lie detector will show a positive reading...Ch. 2.9 - Prob. 115ECh. 2.9 - A communications network has a built-in safeguard...Ch. 2.9 - A slate auto-inspection station has two inspection...Ch. 2.9 - Prob. 118ECh. 2.9 - Suppose that two balanced dice are tossed...Ch. 2.9 - Suppose that two defective refrigerators have been...Ch. 2.9 - Prob. 121ECh. 2.10 - Applet Exercise Use the applet Bayes Rule as a...Ch. 2.10 - Prob. 123ECh. 2.10 - A population of voters contains 40% Republicans...Ch. 2.10 - A diagnostic test for a disease is such that it...Ch. 2.10 - Prob. 126ECh. 2.10 - Prob. 127ECh. 2.10 - Use Theorem 2.8, the law of total probability, to...Ch. 2.10 - Males and females are observed to react...Ch. 2.10 - A study of Georgia residents suggests that those...Ch. 2.10 - Prob. 131ECh. 2.10 - A plane is missing and is presumed to have equal...Ch. 2.10 - A student answers a multiple-choice examination...Ch. 2.10 - Two methods, A and B, are available for teaching a...Ch. 2.10 - Of the travelers arriving at a small airport, 60%...Ch. 2.10 - Prob. 136ECh. 2.10 - Five identical bowls are labeled 1, 2, 3, 4, and...Ch. 2.10 - Prob. 138ECh. 2.11 - Refer to Exercise 2.112. Let the random variable Y...Ch. 2.11 - Refer to Exercise 2.120. Let the random variable Y...Ch. 2.11 - Refer again to Exercise 2.120. Let the random...Ch. 2.11 - A spinner can land in any of four positions, A, B,...Ch. 2 - Show that Theorem 2.7 holds for conditional...Ch. 2 - Let S contain four sample points, E1, E2, E3, and...Ch. 2 - Prob. 145SECh. 2 - Prob. 146SECh. 2 - Prob. 147SECh. 2 - A bin contains three components from supplier A,...Ch. 2 - A large group of people is to be checked for two...Ch. 2 - 2.149 A large group of people is to be checked for...Ch. 2 - Prob. 151SECh. 2 - Prob. 152SECh. 2 - Prob. 153SECh. 2 - a A drawer contains n = 5 different and...Ch. 2 - A group of men possesses the three characteristics...Ch. 2 - The accompanying table lists accidental deaths by...Ch. 2 - Prob. 157SECh. 2 - A bowl contains w white balls and b black balls....Ch. 2 - Prob. 159SECh. 2 - A machine for producing a new experimental...Ch. 2 - Prob. 161SECh. 2 - Prob. 162SECh. 2 - Relays used in the construction of electric...Ch. 2 - Prob. 164SECh. 2 - Refer to Exercise 2.163 and consider circuit B. If...Ch. 2 - Prob. 166SECh. 2 - Prob. 167SECh. 2 - As in Exercises 2.166 and 2.167, eight tires of...Ch. 2 - Three beer drinkers (say I, II, and III) are to...Ch. 2 - Prob. 170SECh. 2 - Prob. 171SECh. 2 - Prob. 172SECh. 2 - Prob. 173SECh. 2 - Prob. 174SECh. 2 - Prob. 175SECh. 2 - Prob. 176SECh. 2 - Refer to Exercise 2.90(b) where a friend claimed...Ch. 2 - Suppose that the probability of exposure to the...Ch. 2 - Two gamblers bet 1 each on the successive tosses...Ch. 2 - Prob. 180SECh. 2 - Suppose that n indistinguishable balls are to be...
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